Networks: structure, evolution & processes

Internet Analytics - Lab 2


Group: P

Names:


Instructions

This is a template for part 3 of the lab. Clearly write your answers, comments and interpretations in Markodown cells. Don't forget that you can add $\LaTeX$ equations in these cells. Feel free to add or remove any cell.

Please properly comment your code. Code readability will be considered for grading. To avoid long cells of codes in the notebook, you can also embed long python functions and classes in a separate module. Don’t forget to hand in your module if that is the case. In multiple exercises, you are required to come up with your own method to solve various problems. Be creative and clearly motivate and explain your methods. Creativity and clarity will be considered for grading.


2.3 Epdemics

Exercise 2.9: Simulate an epidemic outbreak

At day 1, there are almost all susceptibles (in yellow color) and we can observe how the epidemic is expanding between the neighbours of the source node (red colour).

At day 3, the epidemic has started to infect the bridges and therefore other clusters. Some nodes have started to recover (in green).

At day 30, the epidemic has infected almost every node and the majority of them have already recovered from it.


2.3.1 Stop the apocalypse!

Exercise 2.10: Strategy 1

Here we compute the mean of the infections, recoveries and susceptibles in each iteration for each day of the epidemic.
Then, we have decided to fix the number of iterations based on the Coefficient of Variation (CV) of the recoveries at one day (we chose the last day). When CV >= 1, indicates a relatively high variation of the recoveries, while a CV < 1 indicates a low variation. So when we reach CV < 1 we can say that the estimation is accurate.
We have decided to fix a minimum of 7 iterations.

This strategy has decreased the number of people that gets infected (~3000 people less) by the COVID-19 because the number of edges between the nodes (people) have decreased.

On average there is a considerable decreasing on the number of infected people, but it depends a lot on which is the source node (the first infected person), if the nodes is part of a big cluster of nodes or if it is in a small one, in the first case there will be more infections than in the second case, or also if it has been affected for many removed edges.

Exercise 2.11: Strategy 2

As we can see in this graph, we have managed to reach more than 70% of healthy nodes on average.

Here we are going to plot the evolution of the epidemic in our last simulation (58% of the people stayed healthy).

As we can see, it depends a lot in which giant component is the source node. In this case it is in a giant component with a lot of nodes that it much more connected than the giant components where the source nodes of the other simulations are.

We can also see how the removing of the local bridges has affected the connections between the giant components, isolating from of each other.